Dima Arinkin's papers

Papers by Dima Arinkin

My papers on arXiv (some of the older ones are not available on arXiv).

Irreducible connections admit generic oper structures. Preprint arXiv:1602.08989, 18 pp.

Singular support of coherent sheaves and the geometric Langlands conjecture (with D.Gaitsgory). Selecta Math., 21 (2015), no. 1, 1-199. arXiv version.

Formality of derived intersections and the orbifold HKR isomorphism (with A.Caldararu and M.Hablicsek). Preprint arXiv:1412.5233, 23 pp., submitted for publication.

The category of singularities as a crystal and global Springer fibers (with D.Gaitsgory). Preprint arXiv:1412.4394, 80 pp., submitted for publication.

Partial Fourier-Mukai transform for integrable systems with applications to Hitchin fibration (with R.Fedorov). Accepted to Duke Math. Journal, arXiv version, 36 pp.

Derived intersections and the Hodge theorem (with A.Caldararu and M.Hablicsek). Preprint arXiv:1311.2629, 36 pp., submitted for publication.

*-Quantizations of Fourier-Mukai transforms (with J.Block and T.Pantev). Geometric and Functional Analysis, 23 (2013), no. 5, 1403-1482. arXiv version.

Autoduality of compactified Jacobians for curves with plane singularities. Journal of Algebraic Geom., 22 (2013), 363-388. arXiv version.

Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor (with A.Varchenko). In "Configuration Spaces, Geometry, Combinatorics and Topology" edited by A.Bjorner, F.Cohen, C.De Concini, C.Procesi, and M.Salvetti, 2012, 49-53. arXiv version.

When is the self-intersection of a subvariety a fibration? (with A.Caldararu). Advances in Math., 231 (2012), no. 2, 815-842. arXiv version.

An example of Lanlgands correspondence for irregular rank two connections on P¹ (with R.Fedorov). Advances in Math., 230 (2012), no. 3, 1078-1123. arXiv version.

Cohomology of line bundles on compactified Jacobians. Math. Res. Lett. 18 (2011), no. 6, 1215-1226. arXiv version.

Rigid irregular connections on P¹. Compositio Math., 146 (2010), 1323-1338. arXiv version.

Perverse coherent sheaves (with R.Bezrukavnikov). Moscow Math. J. 10 (2010), no.1, 3-29. arXiv version.

Fourier transform and middle convolution for irregular D-modules. Preprint arXiv:0808.0699, 29 pp.

Tau-function of discrete isomonodromy transformations and probability (with A.Borodin). Compositio Math. 145 (2009) 747-772. arXiv version

Moduli spaces of d-connections and difference Painlev\'e equations (with A.Borodin). Duke Math. J. 134 (2006), no. 3, 515-556. PDF offprint, arXiv version.

On λ-connections on a curve where λ is a formal parameter. Math. Res. Lett. 12 (2005), no. 4, 551-565. PDF.

Moduli of connections with a small parameter on a curve. Preprint arXiv:math/0409373, 19 pp.

Appendix to Torus fibrations, gerbes, and duality by R.Donagi and T.Pantev. Mem. Amer. Math. Soc. 193 (2008), no. 901. arXiv version.

Fukaya category and Fourier transform (with A.Polishchuk). Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999), 261-274. arXiv version.

Orthogonality of natural sheaves on moduli stacks of SL(2)-bundles with connections on P¹ minus 4 points. Selecta Math., New Series 7 (2001), 213-239. PDF.

On the moduli of SL(2)-bundles with connections on P¹\{x₁,...,x₄} (with S.Lysenko). Internat. Math. Res. Notices, no. 19 (1997), 983-999. PDF.

Isomorphisms between moduli spaces of SL(2)-bundles with connections on P¹\{x₁,...,x₄} (with S.Lysenko). Math. Res. Lett. 4 (1997), no. 2-3, 181-190. PDF.

Invertible sheaves on the moduli variety of SL(2)-bundles with a connection on P¹ (with S.Lysenko) (Russian). Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, no. 6 (1997), 7-11.
This short note was published via the 'old-fashioned' process, and I do not have it in TeX. Here is the abstract:
We study the moduli stack M of SL(2)-bundles with connections on P¹. These connections are assumed to have poles of the first order at n points, and the conjugacy classes of their residues are fixed. We compute the Picard group of M. In the case of four points, we compute the cohomology groups of invertible sheaves on M.